I posted this problem last night and some one told me I was wrong. Today, two of my group members have the same answers for this problem. Can some one tell us what or where we went wrong?
Using rational zero theorem find all rational zeros
P(x)=3x^3+43x^2+43x+27
Factors: 27, -1, 3, 9, 27
Factors: 3, -1, 3
+-1/3, +-1, +-3, +-9, +-27 possible rational zero for function P(x)
To find the rational zeros of a polynomial using the Rational Zero Theorem, follow these steps:
1. Identify the polynomial and its coefficients. In this case, the polynomial is P(x) = 3x^3 + 43x^2 + 43x + 27.
2. Use the Rational Zero Theorem, which states that if a rational number p/q is a zero of the polynomial, then p must be a factor of the constant term, and q must be a factor of the leading coefficient. In this case, the constant term is 27, and the leading coefficient is 3.
3. Find all possible factors of the constant term (27) and the leading coefficient (3). For 27, the factors are 1, 3, 9, and 27; for 3, the factors are 1 and 3.
4. Form all possible fractions using the factors found in step 3, using both positive and negative versions. Possible rational zeros for the function P(x) are ±1/3, ±1, ±3, ±9, and ±27.
In your case, you correctly applied the Rational Zero Theorem to find the possible rational zeros. The factors you found for the constant term (27) and the leading coefficient (3) are correct. So, the possible rational zeros for the function P(x) are ±1/3, ±1, ±3, ±9, and ±27.
It is important to note that finding the possible rational zeros does not guarantee that these are the actual zeros of the polynomial. To find the actual zeros, you need to further analyze the polynomial using techniques such as factoring, synthetic division, or the use of a graphing calculator.